The marine Controlled Source Electromagnetic (CSEM) method is an important and almost
self-contained discipline in the toolkit of methods used by geophysicists for probing the earth.
It has increasingly attracted attention from industry during the past decade due to its potential
in detecting valuable natural resources such as oil and gas.
A method for three-dimensional CSEM modelling in the frequency domain is presented. The
electric field is decomposed in primary and secondary components, as this leads to a more
stable solution near the source position. The primary field is computed using a resistivity
model for which a closed form of solution exists, for example a homogeneous or layered
resistivity model. The secondary electric field is computed by discretizing a second order
partial differential equation for the electric field, also referred in the literature as the vector
Helmholtz equation, using the edge finite element method. A range of methods for the solution
of the linear system derived from the edge finite element discretization are investigated.
The magnetic field is computed subsequently, from the solution for the electric field, using
a local finite difference approximation of Faraday’s law and an interpolation method. Tests,
that compare the solution obtained using the presented method with the solution computed
using alternative codes for 1D and 3D synthetic models, show that the implemented approach
is suitable for CSEM forward modelling and is an alternative to existing codes.
An algorithm for 3D inversion of CSEM data in the frequency domain was developed and
implemented. The inverse problem is solved using the L-BFGS method and is regularized
with a smoothing constraint. The inversion algorithm uses the presented forward modelling
scheme for the computation of the field responses and the adjoint field for the computation
of the gradient of the misfit function. The presented algorithm was tested for a synthetic
example, showing that it is capable of reconstructing a resistivity model which fits the synthetic
data and is close to the original resistivity model in the least-squares sense.
Inversion of CSEM data is known to lead to images with low spatial resolution. It is well
known that integration with complementary data sets mitigates this problem. It is presented
an algorithm for the integration of an acoustic velocity model, which is known a priori, in the
inversion scheme. The algorithm was tested in a synthetic example and the results demonstrate
that the presented methodology is promising for the improvement of resistivity models
obtained from CSEM data.